Russian Physics Journal

, Volume 59, Issue 8, pp 1153–1163 | Cite as

Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups


The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.


Dirac equation noncommutative integration symmetry algebra 


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia
  2. 2.National Research Tomsk Polytechnic UniversityTomskRussia

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